Criteria for Equilibrium Osmotic Pressure

A system in equilibrium is fully relaxed its state does not change in time. Of course, fluctuations occur on a molecular level but these are random and do not result in changes in the macroscopic properties of the system. For instance, for the liquid-gas equilibrium of a component i, molecules of i are continuously transferred between the two phases but there is no net transport of i from the one phase to the other. 

The requirements for a system to attain equilibrium depend on its interactions with the environment. As we have seen in Section 3.2, the second law of thermodynamics tells us that a process proceeds irreversibly if dS SqlT and that an equilibrium is reached when dS = SqlT. The second law may be combined with expressions for U, H, F, or G to And the appropriate criterion for equilibrium. 

Consider homogeneous closed systems, that is, systems that consist of one phase and that do not exchange matter or electric charge with the environment. Equation 3.4 applied to such systems gives dU=Sq- pdV. A special case is an isolated system that has no interaction whatsoever with its environment, implying that Sq = 0 and pdV = 0. Thus, the system is off-equilibrium when T dS Sq, d5 0 and at 

In general, I/ , V , and can be varied independently and Equation 3.33 therefore holds only if each of the terms on the right-hand side is zero. Hence, 

It may be clear that in the case where electrical work is involved Eqnation 3.34 should be supplemented with / = /P and for heterogeneous systems y = yP. 

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